Stability of a solution to an integral geometry problem in Sobolev norms.
Stable random fields and geometry
Let (M,d) be a metric space with a fixed origin O. P. Lévy defined Brownian motion X(a); a ∈ M as 0. X(O) = 0. 1. X(a) - X(b) is subject to the Gaussian law of mean 0 and variance d(a,b). He gave an example for , the m-dimensional sphere. Let be the Gaussian random measure on , that is, 1. Y(B) is a centered Gaussian system, 2. the variance of Y(B) is equal of μ(B), where μ is the uniform measure on , 3. if B₁ ∩ B₂ = ∅ then Y(B₁) is independent of Y(B₂). 4. for , i = 1,2,..., , i ≠ j, we...
Stationary states
Superconnection currents and complex immersions.
Sur la régularité du profil isopérimétrique des surfaces riemanniennes compactes
On montre que, sur une surface riemannienne compacte, le profil isopérimétrique admet un développement limité à l’ordre en . Lorsque la métrique est analytique, le profil est semi-analytique. Il existe des métriques lisses sur la -sphère dont le profil n’est pas de classe au voisinage de .
Sur la structure des courants positifs fermés
Sur les applications du type
Sur les conditions globales du problème des conditions initiales du cas extérieur
Sur les géodésiques qui coupent un convexe en courbure négative ou nulle
Sur les longueurs des géodésiques dùne métrique à courbure négative dans le disque.
Sur un problème de la métrique angulaire dans la géometrie de Minkowski
Systoles et applications selon Gromov
The behaviour of the total twist and self-linking number of a closed space curve under inversions.
The Bend of Bernstein Polynomials.
The Gauss-Bonnet theorem for Cayley-Klein geometries of dimension two.
The indicator of contact boundaries for an integral geometry problem.
The isoperimetric inequality and the total absolute curvature of closed curves in spheres.
The mean curvature of a Lipschitz continuous manifold
The paper is devoted to the description of some connections between the mean curvature in a distributional sense and the mean curvature in a variational sense for several classes of non-smooth sets. We prove the existence of the mean curvature measure of by using a technique introduced in [4] and based on the concept of variational mean curvature. More precisely we prove that, under suitable assumptions, the mean curvature measure of is the weak limit (in the sense of distributions) of the mean...
The Radon Transform for Forms of Type (1, 1) on a Complex Projective Space.
The Radon Transform for Forms of Type (1, 1) on Complex Projective Space (Erratum).